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An Active Microarchitectured Material that Utilizes PiezoActuators to Achieve Programmable Properties**

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By Yuanping Song, Peter C. Dohm, Babak Haghpanah, Ashkan Vaziriand Jonathan B. Hopkins*

In this paper, a new microarchitectured material is introduced that consists of a large periodic lattice of smallcompliant unit cells (i.e., <5mm) that are independently controlled using piezo actuators, sensors, andmicroprocessors embedded within each cell. This material exhibits desired bulk properties according to controlinstructions that are programmed and uploaded to the material’s microprocessors. Analytical methods are usedto identify optimal design instantiations of the material that achieve programmable properties over ranges ofstrain as high as 9.1% or achieve any desired stiffness over ranges of externally applied stresses as high as10.6MPa without failing. A macro-scale 2D version of the material’s cell is fabricated and controlled to achievedesired stiffness values.

Unlike most microarchitectured materials[1,2] that pas- controller, desired combinations of properties can be actively

sively exhibit their bulk properties based solely on theirmicrostructure’s topology and constituent material proper-ties, the proposed material of this paper (Figure 1) activelyexhibits its properties primarily from its internal piezoactuators, which are driven according to control instructions.Thus, if designers wish to achieve different combinations ofdesired properties (e.g., Young’s Modulus, Poisson’s ratio,density, and damping coefficient), they do not need toredesign or refabricate the mechanical infrastructure of theirinitial design, but can simply reprogram and upload newcontrol instructions to the existing design such that thedifferent combinations of bulk lattice properties can beachieved. And, since such control instructions can be alteredand uploaded in real-time using a centralized master

[*] Prof. J. B. Hopkins, Dr. Y. Song, Dr. P. C. Dohm,Dr. B. HaghpanahDepartment of Mechanical and Aerospace Engineering,University of California, Los Angeles, Los Angeles, California90095, USAE-mail: hopkins@seas.ucla.eduProf. A. VaziriDepartment of Mechanical and Industrial Engineering,Northeastern University, Boston, Massachusetts 02115, USA

[**] This work was primarily supported by the Air Force Office ofScience Research under award number FA9550-15-1-0321.Program officer Byung “Les” Lee is gratefully acknowledged.NSF-CAREER grant number CMMI-1149750 (AV) is alsoacknowledged. Y. Song and Prof. J. B. Hopkins contributedequally to this work. (Supporting Information is availableonline from Wiley Online Library or from the author).

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and continuously tuned or maintained over appreciabledeformations on demand. The proposed material can alsoachieve extreme mechanical properties that cannot beachieved by naturally occurring materials, composites, orother passive microarchitectured materials because theproposed material is energized by a power source (e.g.,batteries or an external power line) that can significantlyamplify the material’s response to mechanical loads.

Some materials already exist with mechanical propertiesthat can be actively tuned.[3] The stiffness properties of anumber of homogeneous solid materials (e.g., ceramics,[4]

polymers,[5] metallic oxides,[6] and shape memory alloys[7,8])can be tuned by actively changing their temperature. Moreadvanced materials that utilize different means of actuationhave been developed to achieve a substantially larger range oftunable stiffness. Magnetic fields have been used to stiffenelastomers loaded with magnetic particles[9,10] as well as softcomposites embedded with magnetorheological fluids.[11]

Electricity has been used to electrostatically increase thestiffness of beams in bending[12,13] as well as lower thestiffness of composites embedded with low-melting-pointmetals via resistance heating.[14] Hydraulic pressure has alsobeen used to stiffen composites filled with fluid[15] andpneumatic pressure has been used to stiffen structures viaparticle jamming.[16,17] A microarchitectured material designwas recently proposed that utilizes electromagnetic locks toachieve discrete stiffness values, which approach continuityas the number of on-off locks within the lattice increases.[18] Akey difference between these materials and the materialproposed here is that the proposed material can beprogrammed to exhibit desired combinations of multiple

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Fig. 1. (a) Active microarchitectured material lattice design, (b) and (c) its cell’s repeated sector, (d) a cross-section of the sector, and (e) a cross-section of the unit cell.

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properties simultaneously (e.g., Young’s Modulus, Poisson’sratio, density, and damping coefficient) that can be main-tained at constant values over appreciable deformations oractively tuned in a purely continuous way according toinstructions uploaded within independently controlled unitcells. Such capabilities would impact advanced applicationsdescribed in Supporting Information.

To understand how the proposed material achievesprogrammable properties, consider the periodic lattice ofunit cells shown in Figure 1a. Each cube-shaped unit cellconsists of the same sector design (Figure 1b and c) repeatedsix times within the cube. At the center of each unit cell is amicroprocessor or integrated circuit (IC) chip, labeled inFigure 1c, that functions as the brain of each cell. Conductivelines, labeled “Power” in Figure 1b, run down the middle oftrapezoid-shaped blade flexures to power the IC chip from anexternal source. The trapezoid-shaped blade flexures aredesigned to deform such that the unit cells are permittedto move with respect to one another as desired, whilesimultaneously constraining the unwanted relative shear andtorsional motions. Note that the lattice’s unit cells jointogether along the top faces of these trapezoid-shapedblade flexures as well as along the top face of each sector’splunger, labeled in Figure 1d. The cross-sectional view ofFigure 1d details how the cell’s IC chip could also beelectrically grounded by an external source. The darkest grayregions, labeled “G” in Figure 1d, are conductive and areconnected to an electrical ground. Note from the isometricview in the top portion of Figure 1d that the two bodieslabeled “G” on either side of the plunger in the bottom portionof the same figure are joined together as part of the same rigidbody with a hole down its central axis through which theplunger is designed to translate. Each sector’s four piezo

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actuators, labeled “Piezo” in Figure 1d, spanbetween this electrically grounded body at oneend and a different conductive electrode at theirother end. These electrodes are wired directly tothe cell’s IC chip via the lines labeled “V” inFigure 1d. If the IC chip imparts a positive ornegative voltage on these “V” lines, the piezoactuators will expand or contract causing theplunger to move down or up, respectively, dueto the fact that the actuators are placed within acompliant transmission mechanism, labeled inFigure 1d. This transmission mechanism causesthe displacement of the plunger to amplify thedisplacement of the actuators, while alsocausing the plunger’s output force capabilityto attenuate the actuators’ output force capabil-ity. This transmission effect is important becausepiezo actuators inherently exhibit abundantoutput force capabilities but do so over limitedranges of strain. Thus, by adjusting the geometryof the transmission mechanism, designers cantune the lattice such that it achieves a usefulrange of programmable properties over a large

range of strains. Note also that the transmission mechanismutilizes notch flexures, labeled “Notch” in Figure 1d, whichcause small localized regions of deformation that maximizethe transmission efficiency of the mechanism by minimizingthe amount of strain energy stored in the compliant structure.Notch flexures also enhance the design’s functionalitybecause they are less likely to cause failure due to bucklingcompared with other flexure element alternatives (e.g., bladeor wire flexures). Note also that the axes of the design’s piezoactuators are aligned along the diagonal directions of thecube-shaped unit cell’s square faces. This alignment allowsthe piezo actuators to be as long as possible such that theirrange of expansion and contraction can be maximized.Although the four piezo actuators are used to drive thesector’s plunger along its axis, a sleeve-like capacitive sensorthat surrounds the plunger could be used to sense its relativedisplacement. As the electrically grounded plunger translatesalong its axis, the conductive region that surrounds thebottom-portion of the plunger, colored yellow in Figure 1d,could be used to supply the unit cell’s IC chip with thenecessary electrical signal to determine the plunger’s relativedisplacement via the line labeled “S.” With the ability toactuate and sense the relative displacement of each sector’splunger, the lattice’s unit cells can independently control theirinteractions using closed-loop control as governed by theinstructions uploaded within each unit cell’s IC chip. Notefrom the cross-sectional view of each unit cell in Figure 1e thata large percentage of the design’s volume is afforded to the ICchips as well as potential antennas, if wireless uploading ofcontrol instructions is desired, and/or batteries, if thematerialis intended to operate in the absence of an external powersource. If such batteries are also rechargeable, the lattice couldbe recharged by cyclically loading the material’s lattice

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externally because the design’s piezo actuators wouldreversibly generate electrical power as they are mechanicallystrained. And, although it may be possible to actively controlthe lattice such that it exhibits isotropic material properties,the geometry of each unit cell possesses the necessary nineplanes of symmetry[19] to passively exhibit cubic materialproperties. Approaches for fabricating this proposed materialare provided in Supporting Information.

The material operates primarily on principles of swarmrobotics[20] in which an overall desired behavior (i.e., a bulkproperty) emerges from the interactions of many smallerentities (i.e., unit cells) that are programmed to obey simpleinstructions relating to the behavior of the other entities inthe swarm (i.e., the lattice of unit cells). Suppose, for instance,every unit cell within a lattice is programmed such thatwhen their plungers are displaced by their neighbor in aparticular direction along their axes, the cell’s piezo actuatorsare instructed to respond by pushing the plungers in theopposite direction. This simple set of instructionswould causethe entire lattice to exhibit a higher Young’s Modulus thanthe lattice would exhibit passively. If, however, the unit cellsare programmed such that the piezo actuators insteadresponded to the displaced plungers by pulling in the samedirection, the overall lattice would achieve a low, zero, or evennegative Young’s modulus. A discussion of different instruc-tions that cause thematerial to exhibit other properties and/or

Fig. 2. (a) Simplified unit cell topology defined by five independent parameters, (b) a plot otopology using an exhaustive sweep of the five parameters, (c) a plot of the maximum tensile astress and strain ranges for the same design instantiations showing two designs that lie

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combinations of these properties is provided in SupportingInformation.

To determine what ranges of properties the lattice topologyof Figure 1 can be programmed to achieve, the geometry ofeach unit cell within the lattice is simplified such that each cellcan be defined by five independent parameters labeled inFigure 2 (i.e., P, Q, H, e, and U). Optimal values for theseparameters can be calculated by modeling each sector asbeam elements that join together at rigid nodes, shown darkgray in Figure 2a. Suppose the beams labeled “Silicon” inFigure 2a possess a Young’s modulus of 190GPa, a shearmodulus of 75GPa, and a yield strength of 7GPa. Supposealso the piezo actuator beams, labeled “Piezo (PZT-5H),”possess a Young’s modulus of 43GPa, a shear modulus of16GPa, a yield strength of 76MPa, a maximum positiveelectric field of 2 kVmm�1, a maximum negative electric fieldof�0.3 kVmm�1, and an axial charge constant of 0.64 nmV�1.The maximum negative and positive strain values that can beachieved by arbitrarily large lattices consisting of such unitcells are plotted in Figure 2b for almost one million differentunit cell design instantiations. These design instantiations,shown as individual blue dots in Figure 2b, were generated byconducting a sweep of all the independent design parameterswithin one of the lattice’s repeating unit cells starting from asmallest allowable feature size and incrementing eachparameter small amounts until the largest geometrically

f the maximum negative and positive strains for every design instantiation of the cell’snd compressive stresses for the same design instantiations, and (d) a plot of the maximumalong the optimal design curve.

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Table 1. Finite element verification of the analytical predictions pertaining to design(1) from Figure 2d with P¼ 0.190mm, Q¼ 0.090mm, H¼ 0.310mm,e¼ 0.011mm, and U¼ 0.290mm.

Analyticalcalculations

Finiteelementresults

Percenterror

Maximum positive strain 0.14% 0.15% 6.67%Maximum negative strain �0.95% �1.05% 9.52%Maximum tensile stress 0.129 MPa 0.121 MPa 6.61%Maximum compressivestress

�0.0194 MPa �0.0181 MPa 7.18%

Table 2. Finite element verification of the analytical predictions pertaining to design(2) from Figure 2d with P¼ 0.120mm, Q¼ 0.040mm, H¼ 0.420mm,e¼ 0.004mm, and U¼ 0.470mm.

Analyticalcalculations

Finiteelementresults

Percenterror

Maximum positive strain 0.95% 0.99% 4.04%Maximum negative strain �6.28% �6.58% 4.56%Maximum tensile stress 0.00843 MPa 0.00827 MPa 1.93%Maximum compressivestress

�0.00126 MPa �0.00124 MPa 1.63%

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compatible feature sizes were reached. The details of thisparameter sweep are discussed in Supporting Information.The lattice’s maximum negative and positive strain valueswere determined by calculating the largest distance the topface of the plunger, labeled in Figure 2a, could be displaced bythe piezo actuators down and up without causing anyelementswithin the sector to yield, buckle, or collide, and thendivide these displacements by the sector height (i.e., 0.5mm).The plunger displacements were calculated using the theoryprovided in Supporting Information. The maximum tensileand compressive stresses that can be resisted by the piezoactuators within the repeating unit cells of an arbitrarily largeperiodic lattice such that each unit cell’s plungers do notdisplace without causing any elements within each unit celldesign to yield, buckle, or collide are plotted in Figure 2c forthe same design instantiations plotted in Figure 2b. Thesestresses were also calculated using the theory provided inSupporting Information. They are significant because theyrepresent the ranges of loading stresses between which theentire lattice could be programmed to respond with anydesired stiffness. Note that the lattice could still achieve aprogrammable stiffness if it were loaded with stresses outsideof this range, but the resulting ranges of achievable stiffnesswould be reduced to finite amounts. Note also that althoughthe strain and stress values in Figure 2b and c were plotted forlarge lattices that consist of 1 mm-sized unit cells, these strainand stress values are independent of both the number of unitcells within the lattice and the size of those unit cells. Optimaldesign instantiations can be identified by plotting the

Fig. 3. (a) A 2D version of the design, (b) a unit cell prototype tested using an Instron machiconstant stiffness (i.e., the slope of the tensile load vs. cell extension lines) via control ov

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maximum stress ranges (i.e., the maximum compressivestresses subtracted from the maximum tensile stresses ofFigure 2c) against the maximum strain ranges (i.e., themaximum negative strains subtracted from the maximumpositive strains of Figure 2b) as shown in Figure 2d.

The optimal design instantiations with the largest ranges ofmaximum stresses and maximum strains lie along the curveshown red in Figure 2d. Two sample designs from this curveare labeled (1) and (2) in Figure 2d. Their predictedperformance calculated via the analytical method of thispaper is provided in Table 1 and 2, respectively. Thisperformance was verified using finite element analysis(FEA) as provided in the same tables. Note that the designwith larger nodes (i.e., design (1)) possesses more errorbecause the analytical method of this paper models thesenodes, shown dark gray in Figure 2a, as rigid bodies.

A 2D version of the 3D lattice of Figure 1 is shown inFigure 3a. A macroscale unit cell from this lattice wasfabricated as a proof of concept (Figure 3b) and programmedto exhibit different constant stiffness values, which manifestas the slopes of the linear trends shown in Figure 3c, over a0.5% strain. An Instron testingmachine was used to collect thedata plotted in Figure 3c. Details pertaining to the design,fabrication, and control of the cell shown in Figure 3b areprovided in Supporting Information.

In summary, this paper proposes a newmicroarchitecturedmaterial that consists of independently controlled unit cellswith microprocessors that can be programmed to drive piezoactuators in a controlled fashion such that the overall lattice

ne, and (c) a plot demonstrating that the unit cell can be programmed to exhibit a desireder a strain of 0.5%.

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exhibits desired bulk properties. Analytical methods arecreated to rapidly calculate and optimize thematerial’s rangesof achievable programmable properties and a macro-scale 2Dversion of the unit cell design was fabricated and controlled toachieve desired stiffness values.

Article first published online: March 29, 2016Manuscript Revised: March 14, 2016

Manuscript Received: December 1, 2015

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